Finite Group DatabasebetaFinite Group Databasebeta| order | 33810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C23⋊#64418) |
| unambiguous semidirect product | C23⋊(C5⋊#64418) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C23×#3862 | C2 |
| Fitting, socle | C5×C72×C23 | D3 |
| LCS | G ▷ C5×C23×#3862 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1610 |
Polycyclic presentation:
2,3,5,23,7^2|b^a=b^2,c^a=c^4,d^a=d^22,e^a=e^2f^3,f^a=e^6f^5,e^b=e^4f^4,f^b=f^21103 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33810, 46);